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01.
arXiv (CS.CV) 2026-06-12

What's Old is New Again: Classical Dimensionality Reduction for Efficient Saliency-Guided Biometric Attack Detection

Saliency-guided training is a paradigm in visual recognition that encourages models to focus on the most relevant image regions during learning. While its application in biometric presentation attack detection (PAD) has shown strong benefits in robustness and generalization, adoption is often limited by the high cost, domain specificity, and limited scalability of existing saliency acquisition methods, such as human annotations over a limited dataset. We present a novel, cost-efficient, and highly-scalable approach to saliency acquisition using maps inspired by classical dimensionality reduction techniques: PCA and LDA. Our proposed methods generate saliency maps directly from raw training data, requiring no human annotation nor domain knowledge. We contextualize the effectiveness of these saliency sources in three saliency-explored domains (iris PAD, synthetic face detection, fingerprint PAD) and demonstrate its scalability in two saliency-novel domains (fingerprint vein PAD and ID card PAD). Across all domains tested, models trained using dimensionality reduction-sourced saliency maps exceed baseline and sometimes SOTA saliency methods without any resource investment or domain-specific tooling. Our findings overcome an important yet unaddressed barrier to saliency-guided training for biometric attack detection and beyond.

02.
arXiv (CS.AI) 2026-06-18

FoMoE: Breaking the Full-Replica Barrier with a Federation of MoEs

arXiv:2606.19025v1 Announce Type: cross Abstract: Pre-training Large Language Models (LLMs) typically demands large-scale infrastructure with tightly coupled hardware accelerators. While increasing model and dataset scale remains the dominant driver of performance, Mixture-of-Experts (MoEs) architectures have recently achieved state-of-the-art results by decoupling parameter count from computational cost. This efficiency enables training massive models on constrained compute budgets, yet it typically requires the high-speed interconnects of a single datacenter. To overcome these physical limits, recent approaches such as DiLoCo and Photon use low-communication data-parallel methods to enable scaling across geographically distributed, weakly connected data centers. However, these methods suffer from a fundamental inefficiency: they require full model replicas at every site, which imposes prohibitive memory constraints and communication overheads. In this work, we introduce FoMoE, a system that breaks the full-replica paradigm by partitioning expert layers across workers. We demonstrate that FoMoE: (I) reduces communication costs by up to 1.42x over efficient baselines and 45.44x over DDP via partial expert replication in the studied regimes; (II) achieves empirical throughput speedups of up to 1.4x through a novel skip-token mechanism; and (III) shows stable routing in the trained proxy regimes and projects the communication/memory benefits to 100B-scale configurations through system modelling.

03.
arXiv (CS.CL) 2026-06-19

CREDENCE: Claim Reduction for Decomposition & Enhanced Credibility – Semantic Metrics and Convergence Analysis

Decomposing compound sentences into atomic, verifiable claims is a prerequisite for reliable automated fact-checking. Prior work has relied on token-overlap (Jaccard) metrics that systematically underestimate decomposition quality for paraphrastic claims, and has lacked formal termination analysis for the repair loop. We present Credence, a revised claim decomposition and evaluation framework addressing both shortcomings. Our contributions are: (1) Semantic-F1: we use BGE-large cosine similarity fidelity metric that resolves Jaccard's penalisation and improves downstream fact-checking accuracy; (2) Convergence theorems: we formally characterise four properties of the repair pipeline, establishing that rule-based repair is monotone and finitely terminating under an oracle parser assumption; LLM-based self-repair is provably non-monotone and requires an early-exit guard; (3) Three evaluation benchmarks spanning social-media, encyclopaedic, and news domains for cross-domain generalisation measurement; (4) Multi-model benchmarking across four decomposer models (3.8B-12B) and a closed API model. Experiments on SocialClaimSplit, WikiSplitBench, and ClaimDecompBench show that Semantic-F1 outperforms Jaccard-F1 by +15-32pp. EPR ranges from 0.94 to 1.00 on SocialClaimSplit and WikiSplitBench, while ClaimDecompBench includes lower base EPR cases (down to 0.824) due to harder news-domain constructions, and rule-repair reduces the Atomicity Violation Rate (AVR) by 47-100% relative to the base model without degrading fidelity.

04.
arXiv (CS.CL) 2026-06-16

Building Customer Support AI Agents at 100M-User Scale: An Evaluation-Driven Framework

The rapid rise in LLM capabilities has made AI agents increasingly viable across a broad range of tasks. Among the most promising applications is building production-ready customer-facing agents, a challenge that demands coordinated excellence in evaluation methodology, context engineering, training, and online measurement. Yet these critical pillars are typically developed in isolation, creating blind spots that only surface after deployment. In this paper, we present a unified framework that bridges offline development with online impact for customer support AI agents at Nubank, a company with 100M+ users. Our approach integrates several key components: (1) structured context engineering tailored to customer support agents, (2) systematic human-in-the-loop prompt iteration, (3) rigorous LLM judge evaluation with measured inter-rater agreement and GEPA optimization for consistency, and (4) ideation-to-production validation. A central insight is that evaluation-pipeline quality directly determines iteration velocity. We present results from five production deployments spanning distinct domains: card delivery, debt management, credit-limit support, card management, and product explanation. These deployments deliver consistent customer-satisfaction gains while substantially accelerating iteration. In our card-delivery deployment, large-scale A/B testing yields a 37 percentage-point improvement in AI transactional Net Promoter Score and a 29 percentage-point gain in self-service rate over prior agent variants, alongside a strong correlation between offline simulation metrics and online outcomes, demonstrating that eval-driven development reliably predicts production impact. On most use cases, AI satisfaction reaches within a few percentage points of expert human agents.

06.
arXiv (CS.LG) 2026-06-15

Testing For Distribution Shifts with Conditional Conformal Test Martingales

arXiv:2602.13848v2 Announce Type: replace Abstract: We propose a sequential test for detecting arbitrary distribution shifts that allows conformal test martingales (CTMs) to work under a fixed, reference-conditional setting. Existing CTM detectors construct test martingales by continually growing a reference set with each incoming sample, using it to assess how atypical the new sample is relative to past observations. While this design yields anytime-valid type-I error control, it suffers from test-time contamination: after a change, post-shift observations enter the reference set and dilute the evidence for distribution shift, increasing detection delay and reducing power. In contrast, our method avoids contamination by design by comparing each new sample to a fixed null reference dataset. Our main technical contribution is a robust martingale construction that remains valid conditional on the null reference data, achieved by explicitly accounting for the estimation error in the reference distribution induced by the finite reference set. This yields anytime-valid type-I error control together with guarantees of asymptotic power one and bounded expected detection delay. Empirically, our method detects shifts faster than standard CTMs, providing a powerful and reliable distribution-shift detector.

07.
arXiv (quant-ph) 2026-06-16

Dressed Floquet scars from protected zero modes in a Rydberg chain

arXiv:2606.15605v1 Announce Type: cross Abstract: In this Letter, we present an approximate analytic construction of two zero quasienergy quantum many-body scars in a periodically driven model of Rydberg atoms on a ring, which persist over a range of driving amplitudes and frequencies for finite sizes. An index theorem protects an exponentially large number (in system size) of exact zero energy modes of the Floquet Hamiltonian in this setting. Unlike most of these zero modes which continuously change with drive parameters, these two quantum many-body scars retain the memory of particular states. They can be expressed as {\it dressed versions} of two contrasting states, the Rydberg vacuum and a unitarily rotated variant of a volume-law scar [Ivanov and Motrunich, Phys. Rev. Lett. {\bf 134}, 050403 (2025)], respectively. We provide an analytic understanding of their existence using a Floquet perturbation theory and show their resilience beyond the perturbative regime using exact diagonalization in finite systems. Our study provides insight into the structure of protected zero modes in interacting Floquet settings.

08.
arXiv (CS.AI) 2026-06-24

No Certificate, No Categorical Speech Act: A Brouwerian Assertibility Constraint for Public Reason

arXiv:2603.03971v3 Announce Type: replace-cross Abstract: Generative AI can convert uncertainty into authoritative-seeming verdicts, intensifying the hypersuasive force of automated speech and displacing the justificatory work on which democratic epistemic agency depends. As a corrective, I propose a Brouwer-inspired assertibility constraint for responsible AI: in high-stakes domains, systems may assert or deny claims only if they can provide a publicly inspectable and contestable certificate of entitlement; otherwise they must return Undetermined. This constraint yields a three-status interface semantics (Asserted, Denied, Undetermined) in which statuses mark entitlement to categorical speech rather than truth values of the underlying world-claim. The semantics cleanly separates internal entitlement from public standing while connecting them via the certificate as a boundary object. It also produces a time-indexed entitlement profile that is stable under numerical refinement yet revisable as the public record changes. I operationalize the constraint through decision-layer gating of threshold and argmax decisions, using internal witnesses (e.g., sound bounds or separation margins where available, and contestable surrogates otherwise) and an output contract with reason-coded abstentions. A design lemma shows that any total, certificate-sound binary interface yields witnessed decidability of the deployed predicate on its declared scope, so Undetermined is not a tunable reject option but a mandatory status whenever no adequate forcing witness is available. By making outputs answerable to challengeable warrants rather than confidence alone, the paper aims to preserve epistemic agency against the persuasive pull of automated speech in public justification.

09.
arXiv (CS.AI) 2026-06-15

The Perceived Fragility of Explanations in Audio Models: Manipulation of Attribution with Unchanged Predictions

arXiv:2606.14466v1 Announce Type: cross Abstract: This paper investigates the fragility of post-hoc explanation methods in audio deepfake detection. While previous work on explanation manipulation focused on images using standard $L_p$ metrics, we introduce a psychoacoustic framework that optimizes inaudible perturbations to decouple model attributions from final classifications. We evaluate this vulnerability across state-of-the-art architectures under strict prediction-preserving constraints. By evaluating the manipulation cost through domain-specific perceptual audio quality metrics alongside explanation alignment criteria, our framework demonstrates that an adversary can systematically distort automated explanation heatmaps while preserving the predicted deepfake label. Full code available at: https://github.com/cncPomper/Audio-XAI

10.
arXiv (CS.LG) 2026-06-11

Urban Heat MiniCubes: An AI-Ready dataset for urban heat research

arXiv:2606.11534v1 Announce Type: cross Abstract: Urban heat is amplified by impermeable surfaces and heterogeneous built environments, yet street-level variability remains difficult to quantify because multi-sensor observations are rarely available in consistent, analysis-ready form at the necessary spatiotemporal scales. We present "Urban Heat MiniCubes," a publicly available, FAIR-oriented dataset designed for machine learning applications in urban heat research. The dataset provides harmonized 90 x 90 km gridded data cubes for 48 cities in the Western Hemisphere spanning 2022-2023, with variables reprojected and collocated to a common grid to reduce preprocessing (e.g., reprojection, resampling, and spatiotemporal alignment). Urban Heat MiniCubes includes two complementary modalities: (i) higher-spatial-resolution, lower-frequency observations from Landsat 8/9 (e.g., surface reflectances) and Sentinel-1 (e.g., synthetic aperture radar backscatter), and (ii) higher-temporal-frequency, coarser observations from GOES-R (e.g., longwave infrared brightness temperatures) and a microwave land surface temperature product. We document variables and metadata and provide technical assessment using inter-variable analyses and autoencoder-based reconstruction-error summaries across pixel classes (e.g., water and cloud). Potential use cases and limitations are also discussed.

11.
arXiv (CS.LG) 2026-06-19

Utility-Aware DRL-Based TXOP Adaptation for NR-U and Wi-Fi Coexistence Networks

arXiv:2605.00457v4 Announce Type: replace-cross Abstract: The coexistence of NR-U and Wi-Fi in the unlicensed spectrum introduces a challenging resource management problem, where heterogeneous channel access mechanisms can lead to unbalanced spectrum utilization and severe Wi-Fi performance degradation. To address this issue, this paper proposes a utility-aware deep reinforcement learning (DRL) framework for adaptive transmission opportunity (TXOP) control in NR-U/Wi-Fi coexistence networks. The coexistence process is formulated as a Markov decision process (MDP), in which the NR-U TXOP duration is treated as a controllable variable for regulating post-access channel occupancy. A deep Q-network (DQN) is then employed to learn adaptive TXOP control policies through online interaction with the coexistence environment. A key feature of the proposed framework is the integration of a configurable reward and criterion design, which enables explicit control of the fairness-efficiency-utility tradeoff. Three operating policies are developed, namely absolute fairness, moderate fairness, and utility-oriented moderate fairness, to characterize different coexistence operating points. Simulation results show that the proposed framework achieves a Jain fairness index above 0.9 under strict fairness control. Compared with the absolute fairness policy, the moderate fairness policy improves aggregate throughput by 68.22%, while the utility-oriented policy achieves a 177.6% improvement under the adopted utility evaluation metric. These results demonstrate that the proposed utility-aware DRL framework provides an effective and flexible solution for adaptive TXOP control and tradeoff management in heterogeneous unlicensed coexistence networks.

12.
arXiv (math.PR) 2026-06-24

Sim-to-Real Betting on the E-Process: Bringing "simulators" to anytime-valid confidence sequences

arXiv:2606.24038v1 Announce Type: cross Abstract: This note describes an integration of the sim-to-real performance estimate with betting (from Chen et al.) and the safe anytime-valid inference (from Ramdas et al.). Using the scaled simulators. The method produces efficient, reliable certificates for the mean estimate, an approach that is especially valuable in robot performance testing. This note gives a primary, self-contained account of the construction; preliminaries of the respective methods are kept at a minimum, and one shall refer to the original works for full detail. Some synthetic examples demonstrating the proposed algorithm can be found at https://github.com/ISUSAIL/Bet4Sim2Real-EProcess.

13.
arXiv (CS.CV) 2026-06-16

Text-Vision Co-Instructed Image Editing

Existing image editing methods can be generally categorized into textual instruction-based and visual prompt-based ones. Textual instructions are semantically expressive, but are limited by the coarse granularity of spatial control of the editing results. In contrast, visual prompts such as drag and point can provide precise spatial guidance, but are limited by the inherent ambiguity in semantic intent. To unify the strength of textual and visual prompts, we present Text-Vision Co-Instructed Image Editing, which jointly models textual instructions as semantic intent and sparse visual instructions as spatial guidance, aiming to achieve precise and intent-faithful image manipulation. To this end, we first construct a textual-visual instruction paired dataset with more than 23K samples derived from dynamic videos, enabling aligned supervision for cross-modal instruction. We then propose TV-Edit, a Textual-Visual instruction unified Editing framework to contextualize drag or point-based visual instructions with image-text semantics and lift them into semantic-aware control representations for pretrained editing backbones. By integrating semantic intent and spatial constraints, TV-Edit leads to more precise spatial control, less instruction ambiguity, and stronger structural consistency than text-only or drag-based alternatives. Finally, we establish TV-Edit-Bench, a deliberately designed benchmark to evaluate semantic faithfulness, spatial alignment, and visual consistency with ground-truth references and controlled textual-visual variations for reliable assessment. Our experiments across multiple editing backbones demonstrate that TV-Edit consistently yields more precise and intent-faithful edits, significantly outperforming state-of-the-art instruction-based and drag-based baselines.

14.
arXiv (CS.CV) 2026-06-19

Timage: A Generative Text-in-Image Paradigm for Fine-Tuning Vision-Language Models

Multimodal Large Language Models (MLLMs) often lose track of the right image regions during fine-grained spatial reasoning, because a textual query rarely carries any explicit geometric anchor into the pixel domain. Prevailing remedies either rewire the model's weights or pad the prompt with verbose instructions, yet neither reliably pins the language to the correct visual coordinates without eroding the backbone's general competence. We introduce Timage, a paradigm that recasts multimodal understanding as an alignment problem solved at the input: the query is drawn, as a typeset overlay, onto the image itself. The placement and appearance of this overlay are produced by a Constrained Schrödinger Bridge (cSB), an entropic optimal-transport sampler that factorizes layout synthesis into two coupled stochastic stages. The first stage, Region Search, transports noise toward query-aligned image zones while obeying a hard occlusion barrier that protects salient foreground content; the second stage, Appearance Shaping, sizes the glyphs through an ``ink-budget'' regularizer so that the rendered text stays legible and visually balanced. The resulting overlay behaves as an explicit attention beacon that channels the model's focus along spatial semantics. On the VMCBench suite, Timage paired with a modest 7B backbone clearly overtakes far larger proprietary systems as well as parameter-tuned baselines. The study positions deliberate input reconstruction as a powerful, architecture-neutral lever for strengthening multimodal reasoning.

15.
arXiv (CS.CV) 2026-06-11

AnchorEdit: Maintaining Temporal Consistency in Multi-turn Image Editing via Causal Memory

Multi-turn image editing is essential for iterative design, yet current models often struggle with identity drift and error accumulation over successive steps. While existing research leverages video priors for consistency, their reliance on bidirectional attention is fundamentally misaligned with the causal, sequential nature of interactive editing. In this paper, we propose AnchorEdit, the first autoregressive (AR) diffusion-based framework designed specifically for high-resolution, long-term multi-turn editing. AnchorEdit bridges the gap between video priors and causal inference through a three-stage training curriculum: identity-preserving sing-turn pretraining, causal AR forcing fine-tuning with a novel self-rollout strategy to mitigate exposure bias, and consistency distillation for efficient 4-step generation. During inference, we introduce a memory mechanism to anchor the initial subject identity and ensure stable extrapolation across extended editing trajectories. To evaluate performance, we provide a new high-resolution multi-turn editing benchmark designed to stress-test long-horizon stability. Extensive experiments demonstrate that AnchorEdit achieves state-of-the-art results, maintaining exceptional subject fidelity and instruction following even over 10+ interaction rounds.

16.
arXiv (CS.AI) 2026-06-16

Agentic Framework for Deep Learning workload migration via In-Context Learning

arXiv:2606.15994v1 Announce Type: new Abstract: Translating deep learning models from PyTorch's flexible, object-oriented design to JAX's functional, stateless setup is usually a manual and error-prone task. Automated migration is challenging because Large Language Models (LLMs) struggle with strict and dynamic API alignment and are prone to mistakes for exacting operations. We propose a fully autonomous system that combines In-Context Learning (ICL) with oracle-driven self-debugging. First, we curated an ICL context that serves as a strict reference for idiomatic JAX styling and test case generation. Second, instead of depending on the LLM to deduce mathematical outputs, we run the source PyTorch modules to get their actual dynamic tensor states. This creates an unchangeable execution oracle. We then use an autonomous agentic loop to synthesize tests based on the oracle data. The test cases are executed repeatedly, and the traceback is sent back to the LLM for self-correction. Ablations show that combining ICL references with oracle grounding and self-debugging greatly outperforms pure instructional and basic agentic baselines. This improvement does not add an excessive computational overhead. Our lightweight pipeline achieves 91% numerical equivalence (compared to baseline: 9%, instruction + self-debugging: 27%) on neural modules, providing a highly reliable, scalable blueprint for cross-framework migration. This has been validated across several state-of-the-art models including SAM (segment anything), T5, Code Whisper amongst others showing high numerical equivalency. Code: https://github.com/AI-Hypercomputer/accelerator-agents/tree/main/MaxCode

17.
arXiv (CS.CV) 2026-06-18

ROSA-TFormer: A Radar-Optical Sensor-Aware Temporal Transformer for Pinus sylvestris Plantation Classification in Northern Shaanxi Using GEE-Derived Sentinel-1/2 Time Series

Accurate identification of Pinus sylvestris var. mongolica plantations is important for monitoring afforestation quality and ecological restoration in northern Shaanxi. This paper proposes ROSA-TFormer, a radar-optical sensor-aware temporal Transformer for P. sylvestris classification using Sentinel-1/2 time-series data generated on Google Earth Engine. The model integrates separate SAR and optical embedding branches, a sensor-aware gate, and temporal attention pooling to capture multi-source seasonal features. Experiments on monthly and half-month point-level datasets show that ROSA-TFormer achieves strong classification performance, with 99.67% overall accuracy, 99.56% macro F1, and 98.91% P. sylvestris F1 on the HalfMonth-dataBig dataset. Spatial block validation and ablation results further indicate the effectiveness of radar-optical temporal fusion and sensor-aware modeling. The results demonstrate the potential of ROSA-TFormer for point-level P. sylvestris plantation classification, while broader wall-to-wall validation remains necessary.

18.
arXiv (math.PR) 2026-06-11

On multidimensional infinite dihedral group extensions of Gibbs Markov maps

arXiv:2601.08961v2 Announce Type: replace-cross Abstract: We obtain a local central limit theorem for cocycles associated with a class of non abelian and non compact group extensions of Gibbs Markov maps. This class consists of multidimensional infinite dihedral groups. Unlike in the set up of the random walks on groups, we cannot use the convolution of measures on the group and instead we resort to an approach based on irreducible representations. Depending on the dimension of the group, we obtain either mixing, and thus ergodicity, or dissipativity. Also, we obtain the asymptotics of the first return time of the group extension to the origin.

19.
arXiv (CS.LG) 2026-06-19

Marginal Advantage Accumulation for Memory-Driven Agent Self-Evolution

arXiv:2606.20475v1 Announce Type: new Abstract: In batch-style trace distillation, the same memory operation may receive contradictory feedback across different batches. Existing methods lack a cross-batch, operation-level evidence accumulation mechanism, making it impossible to distinguish stably effective operations from accidental hits. This paper formalizes the requirement as two structural conditions, alignability and comparability, and proposes Marginal Advantage Accumulation (MAA). MAA constructs differential signals to make them comparable across batches, accumulates signed evidence per operation via EMA, and ensures cross-batch traceability through semantic identity merging. As a post-processing architecture, MAA achieves the best results in 14 out of 16 settings across 4 benchmarks and 4 target models, consistently outperforming existing batch-level distillation baselines and matching or surpassing online alternatives in most settings, while reducing optimization-phase token consumption by approximately 75%.

20.
arXiv (CS.CV) 2026-06-18

SMART: A Flexible, Interpretable, and Scalable Spatio-temporal Brain Atlas from High-Resolution Imaging Data

We introduce SMART, a framework for learning a flexible, interpretable, and scalable spatio-temporal brain atlas from longitudinal high-resolution 3D medical images. Existing approaches to spatio-temporal atlas construction rely on black-box generative models that lack flexibility, limit interpretability, and struggle to scale to high-dimensional data. SMART addresses these challenges by learning a continuous disease-time atlas that decouples global group-wise disease dynamics from their patient-specific anatomical manifestation. Guided by anatomically inspired priors, SMART models interpretable global trajectories of regional progression along a shared disease timeline through region-specific differential equations. Global trajectories are further personalized to individual anatomies via dense diffeomorphic displacements parameterized by a flexible and scalable multi-scale Neural Cellular Automata. Evaluated on five longitudinal MRI datasets in Alzheimer's disease (ADNI-1/GO/2, OASIS-3, AIBL; > 1,300 subjects), SMART produces anatomically meaningful predictions of disease progression and achieves state-of-the-art forecasting accuracy and improved temporal consistency over adversarial and diffusion baselines. Our approach establishes a new paradigm for flexible, interpretable, and scalable modeling of spatio-temporal change in high-dimensional medical image time-series.

21.
arXiv (CS.AI) 2026-06-16

Scalable Circuit Learning for Interpreting Large Language Models

arXiv:2606.16939v1 Announce Type: cross Abstract: A prominent research direction in mechanistic interpretability is learning sparse circuits over LLM components to reveal how they jointly produce model behavior. However, raw neurons are polysemantic, making learned circuits hard to interpret. Sparse autoencoder (SAE) features alleviate this, but their high dimensionality makes existing intervention-based circuit learning methods computationally prohibitive. We propose CircuitLasso, a scalable circuit-learning approach based on sparse linear regression. CircuitLasso recovers circuits whose structural accuracy matches that of state-of-the-art intervention-based methods on the benchmark data, at a fraction of the computational cost. For interpretability, CircuitLasso efficiently uncovers relationships among SAE features, showing how human-interpretable semantic features propagate through the model and influence its predictions. Finally, we validate the utility of our learned circuits by leveraging their insights to achieve comparable performance at substantially lower cost on a domain-generalization task.

22.
arXiv (CS.LG) 2026-06-11

Bernstein-Schur Kernels: Random Features by Sketched Modulation and Radial Randomization

Authors:

arXiv:2606.11255v1 Announce Type: new Abstract: Bernstein–Schur kernels are products of a finite-feature kernel (one with an explicit finite-dimensional feature map) and a completely monotone shift-invariant kernel: nonstationary kernels that fall between the shift-invariant and dot-product templates random features usually exploit, so in general neither Bochner sampling nor polynomial sketching applies to the full kernel directly. We give one random-feature construction for the whole class that randomizes both factors: it sketches the finite modulation and randomizes the completely monotone radial factor, sampling the latter's one-dimensional Bernstein–Widder scale and then applying Gaussian random Fourier features (whose frequency is still $d$-dimensional). The feature dimension is then $Dm$, set by the sketch size $m$ and the radial-draw count $D$, free of the $O(d^2)$ size of the exact modulation feature. Keeping the modulation \emph{exact is the analyzable limit ($m\to\infty$): there we prove unbiasedness, an exact variance for the recommended flat estimator, an expected matrix-Bernstein operator-norm bound (with a matching high-probability tail) controlled by the top eigenvalues of the kernel and modulation Gram matrices together with an intrinsic dimension rather than the crude $N\max_{ij}$ entrywise route, and a deterministic relative-spectral kernel-ridge stability result. By conditioning on the sketch, the doubly-randomized estimator inherits the same intrinsic-dimension operator-norm guarantee plus a single additive sketch term, tunable by $m$ independently of $D$. The motivating instance is the biased $yat$-kernel $k_{yat,b}(w,x)=(w^\top x+b)^2/(\|w-x\|^2+\varepsilon)$, $b\ge0$, whose family span contains the inverse-multiquadric kernel by finite differences in $b$; for it the radial mixture is the IMQ spectral sampler, and one frequency per scale is variance-optimal at a fixed radial-feature budget.

23.
arXiv (CS.CV) 2026-06-15

WAM4D: Fast 4D World Action Model via Spatial Register Tokens

World action models (WAMs) have recently shown promise in jointly modeling future observations and executable robot actions. However, most existing WAMs still operate in 2D video or latent spaces, where visually plausible rollouts miss the 3D spatial constraints and occluded contact geometry required for precise manipulation. While geometric foundation models offer strong priors for recovering dense 3D structure and motion from visual observations, forcing WAMs to predict the dense 4D representation introduces costly geometric decoding and slows down causal action generation. To address the trade-off, we present WAM4D, a fast 4D world action model that uses lightweight spatial register tokens as training-time future-depth readouts to transfer pretrained geometric priors into a causal video-action transformer, then removes the register branch for lightweight action inference. To prevent non-causal shortcuts, we further design causal mixture attention for the Mixture-of-Transformers (MoT) WAM backbone, defining modality-specific visibility among video, action, and geometry tokens. Comprehensive experiments on RoboTwin 2.0 and challenging real-world manipulation tasks show that WAM4D improves spatial consistency and achieves competitive action prediction while maintaining efficient inference.

24.
arXiv (CS.CL) 2026-06-16

MAWARITH: A Dataset and Benchmark for Legal Inheritance Reasoning with LLMs

Islamic inheritance law is challenging for large language models because solving inheritance cases requires complex, structured, multi-step reasoning and the correct application of juristic rules to compute heirs' shares. We introduce MAWARITH, a large-scale annotated dataset of 12,500 Arabic inheritance cases for training and evaluating models on the full reasoning chain: (i) identifying eligible heirs, (ii) applying blocking (\d{hajb}) and allocation rules, and (iii) computing exact inheritance shares. To the best of our knowledge, MAWARITH is the first Arabic corpus and benchmark designed for end-to-end Islamic inheritance reasoning. Unlike prior datasets that restrict inheritance case solving to multiple-choice questions, MAWARITH supports the full reasoning chain and provides step-by-step solutions with justifications grounded in classical juristic sources and established inheritance rules, as well as exact share calculations. This enables models to learn how to generate detailed, step-by-step responses to user queries that reflect real-world Islamic inheritance cases. To evaluate models beyond final-answer accuracy, we propose MIR-E (Mawarith Inheritance Reasoning Evaluation), a weighted multi-stage metric that scores key reasoning stages and captures error propagation across the pipeline. We evaluate six large language models in a zero-shot setting. A commercial model achieves about 90\%, whereas all evaluated open-source models remain below 50\%. Our error analysis identifies recurring failure patterns, including scenario misinterpretation, errors in heir identification, errors in share allocation, and missing or incorrect application of key inheritance rules such as \textquotesingle awl and radd. The MAWARITH dataset is publicly available at https://gitlab.com/nlpresearcher/mawarith.

25.
arXiv (math.PR) 2026-06-15

Longest weakly increasing subsequences of discrete random walks on the integers with heavy tailed distribution of increments

arXiv:2603.29047v2 Announce Type: replace-cross Abstract: We investigate the behavior of the length of the longest weakly increasing subsequences (weak LIS) of $n$-step random walks with nonzero integer increments $k = \pm 1, \pm 2, \dots$ given by a symmetric heavy tailed mass distribution proportional to $|k|^{-1-\alpha}$ for several values of the real parameter $\alpha > 0$ together with that of the simple random walk ($k=\pm 1$), to which the $n$-step heavy tailed walks reduce when $\alpha$ grows large enough that step jumps beyond $\pm 1$ become essentially absent on the scale of $n$. By means of exploratory fits, weighted nonlinear least squares, and nested-model comparisons, we found that the sample average length $\langle{L_{n}}\rangle$ scales like $\langle{L_{n}}\rangle \sim \sqrt{n}\log{n}$ when the distribution of increments has finite variance ($\alpha > 2$) and $\langle{L_{n}}\rangle \sim n^{\theta}$ with a varying exponent $\theta > 0.5$ when the variance is infinite ($\alpha \leq 2$). Distributional diagnostics indicate that the bulk of the $L_{n}$ distribution is very well-approximated by a lognormal model, though systematic deviations are observed in the tails. Our results corroborate and expand upon previous results for the LIS of other types of heavy-tailed random walks and raise a conjecture as to whether the distribution of $L_{n}$ is given, or can be effectively described, by a lognormal distribution.